Template mask lithography is a process where a broad beam of energetic radiation, such as particles, ions, electrons, or energetic neutral particles such as helium or hydrogen atoms, illuminates a template mask, a membrane with a fine pattern of open stencil windows, and beamlets of transmitted particles form a structured beam that transfers the mask pattern to a target substrate. However, the strength of a template mask decreases with increasing pattern density, thereby imposing a limit on the practical pattern density that can be achieved in the printed pattern. To overcome this limitation, a lower density mask pattern can be moved over the target substrate to build up, by superposing the images of the individual exposures, a complex high density image (Wolfe et al., U.S. Pat. No. 6,372,391 (2002)). In that patent, it is disclosed that in a preferred embodiment of that invention, a structured ion beam is scanned by inclining the beam relative to the optical axis of the lithography system using an electrostatic deflector. This technique has several disadvantages including a strong dependence of position on beam energy and the inability to shift the position of a structured beam comprising neutral particles, such as hydrogen and helium atoms. An alternative approach that could circumvent these problems is to move the mask relative to the wafer. This approach, however, requires extremely accurate positioning hardware and thus tends to be costly.